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LLT polynomials, chromatic quasisymmetric functions and graphs with cycles
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
2018 (engelsk)Inngår i: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 341, nr 12, s. 3453-3482Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We use a Dyck path model for unit-interval graphs to study the chromatic quasisymmetric functions introduced by Shareshian and Wachs, as well as unicellular LLT polynomials, revealing some parallel structure and phenomena regarding their e-positivity. The Dyck path model is also extended to circular arc digraphs to obtain larger families of polynomials, giving a new extension of LLT polynomials. Carrying over a lot of the noncircular combinatorics, we prove several statements regarding the e-coefficients of chromatic quasisymmetric functions and LLT polynomials, including a natural combinatorial interpretation for the e-coefficients for the line graph and the cycle graph for both families. We believe that certain e-positivity conjectures hold in all these families above. Furthermore, beyond the chromatic analogy, we study vertical-strip LLT polynomials, which are modified Hall-Littlewood polynomials. 

sted, utgiver, år, opplag, sider
ELSEVIER SCIENCE BV , 2018. Vol. 341, nr 12, s. 3453-3482
Emneord [en]
Chromatic quasisymmetric functions, Elementary symmetric functions, LLT polynomials, Orientations, Unit interval graphs, Positivity, Diagonal harmonics
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Identifikatorer
URN: urn:nbn:se:kth:diva-238893DOI: 10.1016/j.disc.2018.09.001ISI: 000448496500020Scopus ID: 2-s2.0-85053911752OAI: oai:DiVA.org:kth-238893DiVA, id: diva2:1265917
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QC 20181126

Tilgjengelig fra: 2018-11-26 Laget: 2018-11-26 Sist oppdatert: 2018-11-26bibliografisk kontrollert

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